Tropical Cyclone Fina loomed off the coast of the Northern Territory for several days before rapidly strengthening to a Category 3 storm.

It swept on Saturday night between the busy city of Darwin and the sparsely populated Tiwi Islands -- an archipelago about 80 kilometres (50 miles) off the coast -- where wind gusts reached 110 kilometres per hour.

The "very destructive core" of the cyclone has moved away from the Northern Territory, but heavy rain and winds will persist Sunday, Bureau of Meteorology forecaster Angus Hines said.

Northern Territory Chief Minister Lia Finocchiaro said about 19,000 homes and businesses had lost power in the past 24 hours and efforts were being restore it.

She said there was significant debris, including trees and powerlines, and warned people to take care as they moved around.

"In true territory spirit, neighbours are coming out with chainsaws and everyone's chipping in," she said Sunday.

"This cyclone saw a territory that was united and prepared for what was to come, and as a result we've seen largely minimal impact and no injuries."

Footage showed sheets of rain pouring from roofs during the peak of the cyclone, while huge trees toppled into backyards and roads.

A section of roof at the Royal Darwin Hospital collapsed, leaving bricks and debris littering a corridor floor.

The Darwin Airport, which was forced to shut on Saturday, reopened Sunday.

Fina is now moving offshore toward Western Australia, and forecasts say it may intensify to a Category 4 storm.

But weather authorities said Sunday it was unlikely the cyclone would make landfall and would gradually break apart in the coming days.

Researchers have repeatedly warned that climate change amplifies the risk of natural disasters such as bushfires, floods and cyclones.